PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
80012^202063+160560828Lelio R Paula09/2011
80022^202058+85960826Lelio R Paula09/2011
80031576^19021+19021^157660821Serge Batalov05/2014
8004(2^202009+3)/600560807Lelio R Paula03/2012
800510^60776+360777Robert Price01/2011
800610^60776-1481960776Patrick De Geest12/2012
800755*10^60772+760774Robert Price10/2017
8008(6883*2^201869-1)/3560771Lelio R Paula04/2015
8009(27*2^201841-1)/4360760Lelio R Paula01/2014
80102^201822-17760755Lelio R Paula08/2011
8011(13*10^60744+17)/360745Robert Price06/2015
8012(31*2^201754-1)/9960734Lelio R Paula01/2014
8013(26*10^60717-71)/960718Robert Price03/2015
801437^38712-260709Lelio R Paula08/2013
80152^201657-11200360705Enzo Doria05/2014
8016(10^60703+3^60703)/1360702Robert Price01/2013
80172^201622-11281760695Enzo Doria06/2014
80182^201620-1717760694Enzo Doria05/2013
8019(2^201615-3)*6-760693Gilbert Mozzo05/2016
80202^201609-4978960691Henri Lifchitz03/2005
80212^201582-1906160683Enzo Doria05/2013
802243316!3+2760679Robert Price09/2014
8023(509203*2^201564-1)/506760679Lelio R Paula04/2015
80242^201560+10560676Lelio R Paula08/2011
8025(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
80262^201545-1802160672Enzo Doria05/2013
80272^201543+1171560671Lelio R Paula09/2011
80292^201512-11175560662Enzo Doria05/2014
8028p(13013)#/2+6460662Robert Price03/2017
803011^58248+1660660Lelio R Paula05/2013
80312^201496-2760657Lelio R Paula08/2011
80325*10^60655+5760656Robert Price11/2017
8033(7*10^60643+197)/360644Robert Price07/2017
80342^201426-1609760636Enzo Doria04/2013
8035(17*10^60631-11)/360632Robert Price07/2015
80366^77916-7760631Lelio R Paula04/2013
8037(27*2^201410-1)/49160630Lelio R Paula01/2014
80385^86727+9860620Lelio R Paula04/2013
803917^49266-2660620Lelio R Paula05/2013
804020^46589-3360614Lelio R Paula05/2013
80416^77889+6560610Lelio R Paula04/2013
8042139901#+14838760595Nicolas PALAU09/2016
80432^201285-11172360593Enzo Doria05/2014
804446199*2^201268+12964760593Paul Vanderveen11/2016
80463^126991-10060591Lelio R Paula04/2013
80452^201278-11162360591Enzo Doria05/2014
80475^86682-1600460589Enzo Doria05/2014
8048(865*10^60583-1)/960585Robert Price11/2017
8049(58*10^60579+221)/960580Robert Price02/2017
80509*2^201231-560578Lelio R Paula04/2014
80514*10^60572-8960573Robert Price08/2017
8052(78557*2^201207+1)/1306760571Lelio R Paula06/2014
80532^201186-6694560564Lelio R Paula09/2011
80542^201186-9439560564Lelio R Paula09/2011
805565^33403+3260557Lelio R Paula01/2016
8056103^30079+10260545Norbert Schneider10/2016
8057(1000159^10091+1)/100016060541Faysal YAtim08/2008
80582^201098-1771760537Enzo Doria05/2013
8059(3^126881+8)/482960534Lelio R Paula03/2012
80602^201074+7504960530Enzo Doria04/2016
806111^58111-129060517Enzo Doria11/2012
8062(509203*2^201012-1)/960516Lelio R Paula04/2015
80632^200911+571160481Lelio R Paula10/2011
8064(2^200912-3)/2360480Lelio R Paula03/2012
806518^48179-17^4817960478Jean-Louis Charton12/2010
806738^38281-37^3828160476Robert Price09/2012
80664*7^71560-360476Lelio R Paula09/2014
8068(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
8069lucasV(1,2,401712)+260464Mike Oakes01/2017
80702^200833-1849360457Enzo Doria05/2013
807120^46465-504360453Enzo Doria03/2013
80722^200810-1825760450Enzo Doria05/2013
8073((2)^(2*100400-1)+(2)^(100400-1)+1)+2667260447Faysal YAtim04/2018
80745^86466-1433660438Enzo Doria02/2013
8075Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
8076(29*2^200703-1)/23160417Lelio R Paula01/2014
80772^200682-101683160412Paul Bourdelais11/2012
80782^200617-1788160392Enzo Doria05/2013
8079(25^43201+1)/2660391Robert Price06/2013
80812^200609-13360390Lelio R Paula08/2011
80802^200608-1283760390Enzo Doria10/2012
80822^200607-1712160389Enzo Doria05/2013
808311^57975-162060375Enzo Doria11/2012
8084(9913*2^200538-1)/380160369Lelio R Paula04/2015
80855^86342+6460351Lelio R Paula04/2013
8086(14*10^60346-23)/960347Robert Price04/2015
80872^200457-829560344Lelio R Paula09/2011
80886^77546+11360343Lelio R Paula04/2013
809037^38461-36^3846160315Robert Price06/2012
80892^200361-1759360315Enzo Doria05/2013
809110103^15059-10660304Enzo Doria07/2012
80922^200301-1740160297Enzo Doria05/2013
8093(37*10^60290+71)/960291Robert Price04/2015
80942^200266-9439560287Lelio R Paula09/2011
80952^200261-11161360285Enzo Doria05/2014
809646^36238-4560256Norbert Schneider07/2014
809713^54091+9460255Lelio R Paula05/2013
8098311^24171-15460253Enzo Doria07/2012
80992^200120-8108960243Paul Bourdelais01/2012
81003^126262+868060243Lelio R Paula04/2013
810143031!3-5904960239Robert Price12/2015
81022^200100-11126960237Enzo Doria05/2014
8103(29*2^200069-1)/537360225Lelio R Paula01/2014
810420^46283-192360216Enzo Doria03/2013
81052^200011-11207560210Enzo Doria05/2014
81062^200002+7453960207Enzo Doria04/2016
8107(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
8108(28*10^60180+149)/360181Robert Price10/2017
81092^199872+9360168Donovan Johnson06/2008
81106^77321+7760168Lelio R Paula04/2013
8111(86*10^60165-77)/960166Robert Price05/2016
8112(2^199868+78557)/2337360162Lelio R Paula05/2012
81137^71180+8260155Lelio R Paula04/2013
81152^199814-11229560151Enzo Doria06/2014
8114(51^35227-1)/5060151Paul Bourdelais08/2017
811642964!3-8160135Robert Price09/2014
81172^199709-5160119Lelio R Paula05/2011
81182^199700-11162360116Enzo Doria05/2014
8119(15185*2^199681-1)/15960112Lelio R Paula04/2015
81202^199672+253360108Henri Lifchitz09/2004
812120^46198-1160105Lelio R Paula04/2013
81222^199657+9325760103Yves Minet03/2010
81233^125967-11060102Lelio R Paula10/2012
81242^199654-1881360102Enzo Doria05/2013
8125(29*10^60100+19)/360101Robert Price01/2017
81262^199615-2*199615+160091Robert Price04/2018
8127129^28468+28468^12960085Serge Batalov05/2014
81282^199572-1587360078Enzo Doria04/2013
81299*2^199559+760075Lelio R Paula03/2014
81302^199527-11191960064Enzo Doria05/2014
81312^199522+8287560063Lelio R Paula10/2012
81325^85928-7260062Lelio R Paula10/2012
813339^37749+3860062Norbert Schneider05/2014
81346^77182-14360060Lelio R Paula10/2012
81352^199502-214560057Lelio R Paula06/2011
81362^199493+425760054Lelio R Paula06/2011
81372^199488+4075560052Lelio R Paula06/2011
8138(2^199451+9)/2561960037Lelio R Paula02/2012
81392^199425-6160033Lelio R Paula05/2011
8140(85*10^60026+23)/960027Robert Price11/2015
814165^33107+6260021Lelio R Paula01/2016
81422^199362-121560014Lelio R Paula06/2011
81432^199362-11163360014Enzo Doria05/2014
81441537^18832+18832^153760012Serge Batalov05/2014
81452^199324-1743360003Enzo Doria05/2013
814710^60000+20433160001Milton L. Brown04/2006
814810^60000+8712960001Milton L. Brown04/2006
8146143^27838-260001Lelio R Paula10/2017
814910^59999+6519760000Patrick De Geest04/2005
816710^60000-3252960000Patrick De Geest08/2009
8163(10^60000+2249)/960000Makoto Morimoto09/2016
8164((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
8165(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
8166(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
8150(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
8151(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
8152(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
8153(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
8154(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
8155(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
8156(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
8157(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
8158(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
8159(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
8160(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
8161(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
8162(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
817110^59999-51626759999Patrick De Geest06/2009
817020^46116-4159999Lelio R Paula03/2013
8168(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
8169(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
81726^77100-5559996Lelio R Paula10/2012
8174(19*2^199274+1)/16159987Lelio R Paula07/2012
8173(23^44053+1)/2459987Robert Price06/2013
81759^62848+6^62848-2^6284859973Mike Oakes08/2010
817615852^6061+6061^1585259961Hans Havermann08/2016
817719^46880-2059948Lelio R Paula03/2013
81782^199107-1773759938Enzo Doria05/2013
8179(13*10^59928+83)/359929Robert Price09/2016
818110^59913+10893143159914Marisa Kirisame02/2015
818010^59913+4861959914Patrick De Geest04/2016
818210^59913-7412359913Patrick De Geest03/2016
8183t(199528)59890Robert Price01/2015
81842^198903-1790159876Enzo Doria05/2013
81859*10^59862-1959863Robert Price10/2017
8186gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
8187(3^125447+7)/259854Lelio R Paula04/2012
81885^85630+4^(85630-1)59853Robert Price03/2016
81892^198824-213559852Yves Minet06/2013
8190(124^28591-1)/12359851Richard Fischer10/2017
81912^198799-1611759845Enzo Doria04/2013
81927^70811+6^(70811+1)59843Robert Price07/2016
81932^198774-1594559837Enzo Doria04/2013
81942^198753-1587359831Enzo Doria04/2013
8195(31*2^198748-1)/4559829Lelio R Paula01/2014
81962^198725+6959823Lelio R Paula04/2011
8197(68*10^59821+31)/959822Robert Price10/2015
8198(37*25^42785+1867)/859812Curtis Bright05/2015
81993^125354+266059810Lelio R Paula10/2012
8200105^29591-10459810Norbert Schneider08/2013
82014*5^85565-359808Lelio R Paula09/2014
820213963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
8204125330^3+3^12533059798Anatoly F. Selevich06/2010
82032^198643-318959798Yves Minet10/2014
8205(13*10^59797+191)/359798Robert Price08/2017
8206(7*10^59796-1)/359797Erik Branger03/2014
82072^198595+15359784Lelio R Paula04/2011
8208(19*10^59766+161)/959767Robert Price07/2016
82092^198510-196559758Lelio R Paula06/2011
82102^198506-1907759757Enzo Doria05/2013
82112^198484-1600559750Enzo Doria04/2013
82122^198473-1682159747Enzo Doria05/2013
8213(2^198481-5)/2831159745Lelio R Paula02/2012
82142^198400-18959725Lelio R Paula04/2011
82152^198384-1283759720Enzo Doria10/2012
821642694!3-72959719Robert Price09/2014
82172^198320-1871759701Enzo Doria05/2013
821820^45881-118359693Enzo Doria03/2013
82192^198224-685559672Lelio R Paula05/2011
82202^198181-1910159659Enzo Doria05/2013
82215*10^59650+4159651Robert Price08/2017
82222^198149-11221359649Enzo Doria06/2014
82232^198138+7369959646Enzo Doria04/2016
82242^198129-5559643Lelio R Paula04/2011
82255^85318-1463659635Enzo Doria02/2013
8226(2^198119+47)/156093559634Lelio R Paula02/2012
82272^198090-1609759632Enzo Doria04/2013
82289*10^59617+8959618Robert Price11/2016
822942625!3+8159612Robert Price09/2014
82305^85277-8459607Lelio R Paula10/2012
8231(871*10^59599-7)/959601Robert Price11/2017
82322^197984-1824559600Enzo Doria05/2013
82332^197951-213759590Yves Minet06/2013
8234(38*10^59589+187)/959590Robert Price11/2017
823566^32749-65^3274959589Robert Price09/2013
82365*10^59586-359587Dmitry Domanov11/2010
8237(35*10^59584-197)/959585Robert Kinser10/2017
82382^197932-395959584Yves Minet04/2017
82392^197909-1896159577Enzo Doria05/2013
8240(3^124871+2)/4503159574Lelio R Paula04/2012
82412^197872+8159566Henri Lifchitz10/2005
82422^197873-1846959566Enzo Doria05/2013
8243(22*10^59558-31)/959559Robert Price04/2015
82452^197840-46559556Lelio R Paula05/2011
8244(31*2^197856-1)/388960559556Lelio R Paula01/2014
82462^197808-1780559547Enzo Doria05/2013
82472^197781-1790559539Enzo Doria05/2013
82482^197777-1747359537Enzo Doria05/2013
82496^76507-14959535Lelio R Paula10/2012
825018^47420+2359526Lelio R Paula03/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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